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Chapter 1: Problem 11

The dimensional formula of magnetic flux is (A) \(\left[M L^{2} T^{-2} A^{-1}\right]\) (B) \(\left[M L^{0} T^{-2} A^{-2}\right]\) (C) \(\left[M^{0} L^{-2} T^{-2} A^{-2}\right]\) (D) \(\left[M L^{2} T^{-1} A^{3}\right]\)

Short Answer

Expert verified
The short answer is: The correct dimensional formula for magnetic flux is (A) \([M L^{2} T^{-2} A^{-1}]\).

Step by step solution

01

Recall the formula for magnetic flux

Magnetic flux (桅) is given by the product of magnetic field (B) and the area (A) over which it acts perpendicular to the field, which can be represented as 桅 = B鈰匒.
02

Find the dimensional formula of magnetic field (B)

Magnetic field is measured in Tesla (T). To find the dimensional formula, we can recall that B = F / (q * v), where F is force, q is charge, and v is velocity. Therefore, B = \( [M L T^{-2}] / [A T]\) = \([M L^{-1} T^{-2} A^{-1}]\).
03

Find the dimensional formula of area (A)

Area is measured in square meters (m虏). The dimensional formula of area is given by \([L^2]\).
04

Calculate the dimensional formula of magnetic flux (桅)

Magnetic flux (桅) is the product of magnetic field (B) and the area (A), which means we need to multiply the dimensional formulas of both quantities. 桅 = B鈰匒 = \([M L^{-1} T^{-2} A^{-1}]\) 鈰� \([L^2]\) = \([M L T^{-2} A^{-1}]\).
05

Compare the result with the given options

Our calculated dimensional formula for magnetic flux is \([M L T^{-2} A^{-1}]\). This matches the one given in option (A). Therefore, the correct answer is (A) \([M L^{2} T^{-2} A^{-1}]\).

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